II.
MICROWAVE GASEOUS DISCHARGES
Staff:
Professor S. C. Brown
Professor W. P. Allis
M. A. Biondi
E. Everhart
M. A. Herlin
Donald E. Kerr
A. D. MacDonald
Microwave Breakdown in Air. Breakdown has been measured in TM0 10 -mode
cavities which are long enough to require the non-uniform field theory
reported in the last progress report. These results extend the measurements of the high-frequency ionization coefficient to nearly the full
range available without increasing the magnetron power. The final
complete set of curves for air is shown in Fig. II-1. A technical report
on this subject is being prepared.
U)
I0
oz
0
N
z
0
Z.
10
100
1000
E/p (VOLTS/cn-mm Hg)
Fig. II-1.
1o000
High frequency ionization coefficient
in (ionization/volts2 ) as a function
of E/p (volts 1 cm-mm Hg) and ph (mm-cm).
Microwave Breakdown in Helium. The ionization coefficient t has been
derived for helium treated with mercury, from the Boltzmann transport
equation on the basis of kinetic theory. The derivation gives
S= v/DE 2 , where v is the ionization rate per electron, D is the
-7-
_rr;
- -.
__.~.-._irr
-- ~--- -L--.-----.
l X--XII ^Il------ -l.-*rL ---~-~_Y-~I_
FL-_I-C-------II---LI~I~- *i
diffusion coefficient of electrons in the gas, and E is the r.m.s. value
of the electric field.
For the case where the probability of collision is inversely
proportional to the electron velocity, v, kinetic theory gives
4W t2b Vc3 -dz
3-A 2
dz
ni=
e-2
z M(aO,,z) +
(
M(a-1 ,,z
2
()
z=z
a
Z=Za
/=
where
1
2.3710 p
2
3mA
M1
%Ii
b
=
+
j2
z
=
9.20 b * ( )
a
=
.75
62 + (60T )j
(1 - -)
;
p is the pressure in mm of mercury, m is the mass of the electron, M the
mass of the atom, n the electron density, 2 is a factor which depends
on the geometry of the cavity, and X is the free-space wavelength of the
electric field; z. and v c refer to the values of these quantities for
electronic energies equal to the excitation energy. M(a,,,z) is the
confluent hypergeometric function in a and y, and C is a constant
depending on boundary conditions. One also obtains
nD
=....2
3(Ctb)f
r
e
(
M(l,+,z) + ~2 M(a-,
z
-8-
d
.
Dividing the ratio of (1) and (2) by E2 , one obtains
=
1
1
CAE)2
M(a
a z ,Zc
c C
-
The expression so obtained is not strictly accurate, however,
since the probability of collision is not hyperbolic for all energies but
is as shown in Fig. 11-2.
10
C
18U
14-
108
64
2I
8
2
4
6
Fig. 11-2.
8
10 12 14
(VOLTS)
16
18 20 22 24___26 28 30 32 34
Probability of collision in helium as
a function of energy, at 1 mm pressure.
The effect of the slower electrons will be noticeable at the
higher pressure ranges, so that a correction may be made in this case.
Since nD is an integral over the distribution function from zero energy
to the excitation energy, we may use the distribution function obtained
for constant collision probability (see last progress report) for the
integral from zero to two volts and that of Eq. (2) for the remainder.
obtained. The breakdown
This has been done, and an expression for
condition as obtained from the diffusion equation is that
= l& 2 . Thus
may be predicted for a given cavity and given frequency as a function
Z
of E/p.
Experinental. The breakdown of pure helium treated with mercury has been
measured at 3000 Mc. Reproducible results were obtained after considerable
care was taken vith the vacuum system - the cavities being made of 0.F.H.C.
The whole vacuum system was
copper with glass-kovar coupling leads.
and
distilled mercury was used to
several
days
outgassed over a period of
-9-
1L__YIII__LLIIIIIIII_---( ^---LII.^--L.~11s1
-11-.---X~1~
.^l-~l1 111111-11_
.-~---~__ll-s~ LX
introduce a small amount of mercury vapor into the helium. The cavity was
a short cylinder operating in the TMO 10 -mode, the power being supplied by
an S-band c-w magnetron. A radioactive source was placed near the cavity
to provide electrons. The electric field was slowly increased until
breakdown was indicated on a transmission meter showing a mismatch.
Figure II-3 shows the experimental points along with the theoretical values of J. The work is continuing with more cavities and other
gases.
.2
10
10
AfJ
-4
16
L-'
Fig. II-3.
%CM-mm i
Ionization coefficient in helium.
Measurements of the Ambipolar Diffusion Coefficient in Helium. In the
last progress report calculations to show the necessary gas purity for
accurate data were given. A vacuum system capable of maintaining the
and 10- 6
desired purity has been built. The system holds at between 10
mm Hg pressure indefinitely when isolated from the pumps so that no
appreciable contamination of the helium occurs during the several hours
required to take data. Several runs have been made; the data from a
typical run are plotted in Fig. 1I-4. The data resemble quite closely
100 0
E
E
o 'r.
HELIUM.-"
90 0 80
70P0
60
)o
0-
D
* 1
0
50
0o-0
40
30
0
20
10 0o-V
,
-
A
13
Ie
14II
if I7
0
0
IV
C6V
1
p(mm-H4
Fig. 11-4.
Extrapolated value of D p from
theoretical I+ at 760 m9 pressure.
the curve given in the October 1947 Progress Report. The additional
purity obtained seems to have resulted in a lowered diffusion rate as
predicted.
Comparison of these data with other measurements can be
achieved from the relation between Da and the positive ion mobility, p+:
D
D+_ + D_ +
P+ + -
a
(D+/ + + D_/ _)+
.
Since both positive ions and electrons are at room-temperature energy
in this experiment; we have the result from kinetic theory
D+
4+
D_
._.
-11-
kT
e
........ 1.,..~.I--~,
Da
--lp- ------~---1---~1-1----- ------~--I -----~.-- -1~.1-----1------
..
l"--
DkT
+_
_e
Comparison of the measured value of Da with the mobility
measurements of Tyndall and Powell1 in helium at 760 mm pressure
indicates a difference of a factor of two between the two measurements.
2
However, the comparison of Da with Massey and Mohr's theoretical calculation of t+ in helium at 760 mm pressure gives good agreement in the limit
of zero pressure (cf. Fig. 11-4). The departure of the experimental data
from theory may be due to the action of a removal process other than
ambipolar diffusion.
Some preliminary studies on neon have been made. Since diffusion
in neon should be slower than in helium other removal processes should
show up more clearly in the data. Analysis of the data indicates that a
low-energy recombination between electrons and positive ions is taking
place in addition to the usual diffusion. Observation of recombination
light for at least 300 Ilsec after the discharge is terminated supports
this hypothesis. As yet insufficient time has been available to correlate
the variation in recombination light intensity with the electron density
measured in the microwave experiment.
It is planned to study the low-energy recombination in neon
in more detail. The resulting information should enable us to predict
the importance of this recombination in helium and to correct the data
to achieve better agreement with the theoretical value of Da*
1.
2.
A. M. Tyndall and C. F. Powell, Proc. Roy. Soc., A134, 125 (1931).
H. S. W. Massey and C. Mohr, Proc. Roy. Soc. A144, 199 (1934).
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~-"~'l~ii-